In such a lamp assembly, which is known from WO 2005/024898 A2, the light source is a LED. Part of the light from the light source is directly emitted in forward directions, whilst the other part of the light from the light source is reflected in forward directions by the reflector. By using such a lamp assembly, a spot-like light emission is obtained. While in some applications such directed light is useful, in other applications the spot-like emission is highly undesirable. These applications require a GLS-like light distribution. However, since LEDs emit only in a half sphere, a GLS-like light distribution with a more or less omnidirectional light emission cannot be obtained with the known lamp assembly.